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<div id="breadcrumbs" style="display:none"><a href="simulasi_skenario.html">Scenario Simulation</a> &gt; <a href="pengaturan_skenario.html">Scenario Setting</a></div>

<div id="printheader"><h1 class="p_Heading1"><span class="f_Heading1">Transition Probability Matrix</span></h1>
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   <h1 class="p_Heading1"><span class="f_Heading1">Transition Probability Matrix</span></h1>

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<p style="text-align: justify; line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">The process of land use changes to be simulated follows Markov Chain, in which transition to land use in the next time step only depends on the current land use and the probability of change. The probability of each pair of land use class is compiled as Transition Probability Matrix (TPM), which in the case of stationary land use change process derived solely from the past Land Use Transition Matrix (LUTM).</span></p>
<p style="text-align: center; line-height: 1.15;"><img src="clip0052.png" width="383" height="187" alt="clip0052" style="border:none" /></p>
<p style="text-align: center; line-height: 1.15;"><img src="clip0053.png" width="387" height="401" alt="clip0053" style="border:none" /></p>
<p style="text-align: center; line-height: 1.15; margin: 0px 0px 8px 0px;"><img src="clip0054.png" width="471" height="143" alt="clip0054" style="border:none" /></p>
<p style="text-align: justify; line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">The transition probability matrix is calculated by normalize each row of land use transition matrix to sum up to 1. The existing land use (L) in 1999 changed to land use in 2009 through the transition probability matrix (P), or mathematically it can be written as follows:</span></p>
<p style="text-align: center; line-height: 1.15; margin: 8px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri; font-weight: bold;">L(</span><span style="font-size: 16px; font-family: calibri; font-style: italic; font-weight: bold;">t</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">+1) = L(</span><span style="font-size: 16px; font-family: calibri; font-style: italic; font-weight: bold;">t</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">) x P(</span><span style="font-size: 16px; font-family: calibri; font-style: italic; font-weight: bold;">t</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">)</span></p>
<p style="line-height: 1.15; margin: 8px 0px 0px 0px;"><span style="font-size: 16px; font-family: calibri; font-weight: bold;">Information:</span></p>
<p style="line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">L (</span><span style="font-size: 16px; font-family: calibri; font-style: italic;">t</span><span style="font-size: 16px; font-family: calibri;">) is a row vector or fraction land uses at time </span><span style="font-size: 16px; font-family: calibri; font-style: italic;">t</span></p>
<p style="line-height: 1.15; margin: 0px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri;">P (</span><span style="font-size: 16px; font-family: calibri; font-style: italic;">t</span><span style="font-size: 16px; font-family: calibri;">) is the Transition Probability Matrix (TPM) matrix at time </span><span style="font-size: 16px; font-family: calibri; font-style: italic;">t</span></p>
<p style="text-align: justify; line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">If the process of land use changes in the following time steps is stationary, the Transition Probability Matrix is constant over time, i.e., </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">P</span><span style="font-size: 16px; font-family: calibri;">(</span><span style="font-size: 16px; font-family: calibri; font-style: italic;">t+i</span><span style="font-size: 16px; font-family: calibri;">) = </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">P</span><span style="font-size: 16px; font-family: calibri;">(t) = </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">P</span><span style="font-size: 16px; font-family: calibri;">. Otherwise, we can apply some particular scenarios in two ways:</span></p>
<p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 0px 0px;"><span style="font-size:16px; font-family: 'calibri';color:#000000;display:inline-block;width:19px;margin-left:-19px">1.</span><span style="font-size: 16px; font-family: calibri;">By altering the probability or rate of conversion from one particular land use type to another through the modification of the Transition Probability Matrix at a particular time step.</span></p><p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 8px 0px;"><span style="font-size:16px; font-family: 'calibri';color:#000000;display:inline-block;width:19px;margin-left:-19px">2.</span><span style="font-size: 16px; font-family: calibri;">By determining the converted areas (either in hectares or in fraction) in the future through the modification of the Land Use Transition Matrix at a particular time step.</span></p><p style="text-align: justify; margin: 0px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri;">As a default abacus always offer the constant TPM and </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">L</span><span style="font-size: 16px; font-family: calibri; font-style: italic;">(t+1) </span><span style="font-size: 16px; font-family: calibri;">based on the constant TPM, if we would like to simulate stationary process scenario, then no modification is necessary. However, if we want to simulate particular scenarios we need to modify either the TPM or the LUTM in hectares of LUTM in fraction. As an illustration, a future scenario of enforcement of law through policy and action to halt deforestation of Undisturbed forest for this particular landscape can be done by one of the following:</span></p>
<p style="text-align: justify; padding: 0px 0px 0px 24px; margin: 0px 0px 0px 24px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:24px;margin-left:-24px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">Changing the first row of the TPM for t+1 or P(t+1).</span></p><p style="text-align: justify; padding: 0px 0px 0px 24px; margin: 0px 0px 0px 24px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:24px;margin-left:-24px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">Changing the first row of the LUTM for t+1 or L(t+1) to have all the total area of Undisturbed forest in the first cell and all the rest in the first row zero.</span></p><p style="text-align: justify; padding: 0px 0px 0px 24px; margin: 0px 0px 8px 24px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:24px;margin-left:-24px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">Changing the first row of the normalized LUTM for t+1 or L(t+1) to 1 in the first cell and 0 for the rest of the cells in the first row.</span></p><p style="text-align: center; line-height: 1.15; margin: 0px 0px 13px 0px;"><img src="clip0055.png" width="550" height="164" alt="clip0055" style="border:none" /></p>
<p style="text-align: justify; line-height: 1.15; margin: 8px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri;">Scenario of policy that allows establishment of oil palm only from shrubs can be captured by setting all the cells in 5</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">th</span><span style="font-size: 16px; font-family: calibri;"> column to 0 except for that in the 6</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">th</span><span style="font-size: 16px; font-family: calibri;"> row, however those other rows which are affected by the changes such that the sum is not equal to 1 anymore has to be adjusted. For the purpose of REDD+, then for all forest classes and other land use types that has higher C‐stock than Oil palm should perhaps stay as they are, and therefore shift and add the number in each cell in the 5</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">th</span><span style="font-size: 16px; font-family: calibri;"> column (except for the 6</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">th</span><span style="font-size: 16px; font-family: calibri;"> row) to the number in each associated the diagonal cell, e.g., for Logged‐over forest (2</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">nd</span><span style="font-size: 16px; font-family: calibri;"> row), change the 5</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">th </span><span style="font-size: 16px; font-family: calibri;">column cell to 0 and add 0.1111 to the 2</span><span style="font-size: 16px; font-family: calibri; vertical-align: super;">nd</span><span style="font-size: 16px; font-family: calibri;"> column, which becomes 0.4167+0.1111 = 0.5278.</span></p>
<p style="text-align: justify; line-height: 1.15; margin: 0px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri;">Please note that most likely the scenarios are varied across zones. In the case of legal zoning of forest as is in the Indonesian case, the conservation areas should have different scenarios from production forest and from other, for instance. Zonation based on soil types, i.e., mineral soil and peatland could be very instrumental in some areas in Indonesia where peatland is extensive and under threat while we know that emissions caused by land use changes on peatland could be much higher than those in mineral soils.</span></p>
<p style="line-height: 1.15;"><span style="font-size: 16px; font-family: calibri; font-weight: bold;">How to get Transition Probability Matrix (TPM):</span></p>
<p style="text-align: justify; line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">Click </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">scenario simulation</span><span style="font-size: 16px; font-family: calibri;"> button from main menu </span><span style="font-size: 15px; font-family: Wingdings;">&rarr;</span><span style="font-size: 16px; font-family: calibri;"> </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">scenario setting </span><span style="font-size: 16px; font-family: Wingdings; font-weight: bold;">&rarr;</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;"> Transition Probability Matrix (TPM)</span><span style="font-size: 16px; font-family: calibri;">, or expands the tree menu on the structured menu frame (on the left side by default) click </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">+scenario simulation </span><span style="font-size: 15px; font-family: Wingdings;">&rarr;</span><span style="font-size: 16px; font-family: calibri;"> </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">+scenario setting </span><span style="font-size: 16px; font-family: Wingdings; font-weight: bold;">&rarr;</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;"> Transition Probability Matrix (TPM)</span><span style="font-size: 16px; font-family: calibri;">. If the frame is empty, see how </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">Iteration Setting</span><span style="font-size: 16px; font-family: calibri;"> for generating the scenario.</span></p>
<p style="text-align: center; line-height: 1.15;"><img src="clip0056.png" width="652" height="261" alt="clip0056" style="border:none" /></p>
<p style="text-align: center; line-height: 1.15; margin: 0px 0px 13px 0px;"><span style="font-size: 16px; font-family: calibri;">Access Transition Probability Matrix (TPM)You can start to modify the scenario by editing the matrix table.</span></p>
<p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 0px 0px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:19px;margin-left:-19px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">The sum of each row values should be equal to 1 (slide the table to the right to see the total of each row values).</span></p><p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 0px 0px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:19px;margin-left:-19px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">Select the iteration period to be modified.</span></p><p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 0px 0px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:19px;margin-left:-19px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">After the editing the “update model” button (above the table) will become enabled.</span></p><p style="text-align: justify; padding: 0px 0px 0px 19px; margin: 0px 0px 8px 0px;"><span style="font-size:16px; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:19px;margin-left:-19px">&#8226;</span><span style="font-size: 16px; font-family: calibri;">You should click the “update model” button after finishing the modification on that iteration period.</span></p><p style="text-align: justify; line-height: 1.15; margin: 0px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri; font-weight: bold;">Note</span><span style="font-size: 16px; font-family: calibri;">: If you plan to modify the scenario on more than one period, the modification should be start from the earlier iteration period (otherwise, the modified scenario on the later period will overwrote by the previous one).</span></p>
<p style="text-align: justify; line-height: 1.15; margin: 0px 0px 8px 0px;"><span style="font-size: 16px; font-family: calibri; font-weight: bold;">TIPS</span><span style="font-size: 16px; font-family: calibri;">: you can highlight the row header of a land use system and right click, then click</span><span style="font-size: 16px; font-family: calibri; font-weight: bold;"> “set no conversion”</span><span style="font-size: 16px; font-family: calibri;"> to set the </span><span style="font-size: 16px; font-family: calibri; font-weight: bold;">no conversion </span><span style="font-size: 16px; font-family: calibri;">scenario from the highlighted land use system.</span></p>
<p style="text-align: center; line-height: 1.15; margin: 0px 0px 8px 0px;"><img src="clip0057_zoom90.png" width="643" height="346" alt="clip0057" style="border:none" /></p>
<p style="text-align: center; line-height: 1.15;"><span style="font-size: 16px; font-family: calibri;">Modify Transition Probability Matrix (TPM)</span></p>

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